Question

In: Statistics and Probability

10. The data below shows the high temperatures and the times​ (in minutes) runners who won...

10. The data below shows the high temperatures and the times​ (in minutes) runners who won a marathon. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using a=0.05. Is there sufficient evidence to conclude that there is a linear correlation between temperature and winning​ times?

Temperature_(x)             Time_(y)

56           148.824

60           145.072

45           144.768

63           148.851

70           148.546

74           148.019

52           147.065

57           146.845

What are the null and alternative​ hypotheses?

Construct the scatterplot.

The linear correlation coefficient r is _____

(Round to three decimal places as​ needed.)

The test statistic t is _____

(Round to three decimal places as​ needed.)

The​ P-value is ______

(Round to three decimal places as​ needed.)

Because the​ P-value is (Less/greater) than the significance level 0.05​, there (is not/ is) sufficient evidence to support the claim that there is a linear correlation between between temperature and winning times for a significance level of alphaequals0.05.

Does it appear that winning times are affected by​ temperature?

No​, because there is not a linear correlation between the two variables.

Yes​, because there is a linear correlation between the two variables.

Yes​, because there is not a linear correlation between the two variables.

No​, because there is a linear correlation between the two variables.

Solutions

Expert Solution

Sol:

perform hypothesis test for correlation in R

Rcode is

Temperature_x <- c(56,60,45,63,70,74,52,57)

Time_y <- c(148.824,145.072,144.768,148.851,148.546, 148.019, 147.065,146.845)
plot(Temperature_x,Time_y)   
cor.test(Temperature_x,Time_y)

null and alternative​ hypotheses

Ho:

Ha:

Construct the scatterplot.

The linear correlation coefficient r is

r=0.583

The test statistic t is _

t=1.756

p=0.13

Because the​ P-value is (greater) than the significance level there (is not) sufficient evidence to support the claim that there is a linear correlation between between temperature and winning times for a significance level of alpha equals 0.05.

Does it appear that winning times are affected by​ temperature?

No​, because there is not a linear correlation between the two variables.

orchestra answered 2 years ago
Next > < Previous

Related Solutions

The data below shows the high temperatures and the times​ (in minutes) runners who won a...
The data below shows the high temperatures and the times​ (in minutes) runners who won a marathon. Answer parts ​a-c. Temperature​ (x) 5858 63 50 62 72 73 50 57 Time​ (y) 1145.882 146.683 145.931 146.604 147.965 144.267 148.503 147.643 a. Find the value of the linear correlation coefficient r. b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using alpha=0.05 c. Is there sufficient evidence to conclude that there...
High daily temperatures and times (in minutes) were given for women who won the New York...
High daily temperatures and times (in minutes) were given for women who won the New York City marathon in recent years. Results are listed in the table below. Is here a correlation between temperature and winning time? Use α=.05. What is the best predicted finishing time for a day with a high temperature of 70° F? x(° F) 55 61 49 62 70 73 51 57 y(minutes) 145.3 148.7 148.3 148.1 147.6 146.4 144.7 147.5 r: critical value: Significant linear...
Data are provided to you on test completion times (in minutes) for students who participated in...
Data are provided to you on test completion times (in minutes) for students who participated in a one-hour review class before test number 1 and for these same students who were also administered test number 2 a month later. However, they did not participate in the review class before test number 2. The goal here is to determine whether there is a significant difference in the test completion time between the students when they had the review class compared to...
6. Listed below are actual high temperatures and the high temperatures that were forecast five days...
6. Listed below are actual high temperatures and the high temperatures that were forecast five days earlier. Use a .05 significance level to test the claim of a zero mean difference between the actual high temperatures and the high temperatures that were forecast one day earlier. Use our 4-step procedure. This is a matched or paired samples hypothesis test. Actual high: 80 77 81 85 73 High forecast one day earlier: 78 75 81 85 76 Step 1: Ho____. Ha:...
Given below is simple random sample data for wait times, in minutes, for a call center....
Given below is simple random sample data for wait times, in minutes, for a call center. At the 98% confidence level, calculate the confidence interval estimate for the variance in wait time for the population of all calls at the call center. Assume the population is normally distributed. 12.1 11.5 13.4 16.2 11.3 12.2 11.3
IN JAVA Lab 10 This program reads times of runners in a race from a file...
IN JAVA Lab 10 This program reads times of runners in a race from a file and puts them into an array. It then displays how many people ran the race, it lists all of the times, and if finds the average time and the fastest time. In BlueJ create a project called Lab10 Create a class called Main Delete what is in the class you created and copy the Main class below into the file. There are 7 parts...
The data below represent commute times​ (in minutes) and scores on a​ well-being survey. Complete parts​...
The data below represent commute times​ (in minutes) and scores on a​ well-being survey. Complete parts​ (a) through​ (d) below. Commute Time​ (minutes), x 5 15 25 40 60 84 105 ​Well-Being Index​ Score, y 69.2 68.1 67.2 66.5 65.3 64.7 62.8 ​(a) Find the​ least-squares regression line treating the commute​ time, x, as the explanatory variable and the index​ score, y, as the response variable. y = [ ] x + [ ] ​(b) Interpret the slope and​ y-intercept,...
Two data sets are given below, each representing times (in minutes) to complete a given task...
Two data sets are given below, each representing times (in minutes) to complete a given task for two different samples of students. Data Set A: 3.1, 4.7, 7.3, 8.1, 8.1, 8.7, 8.8, 9.1, 9.1, 9.2 Data Set B: 5.2, 5.6, 5.8, 6.9, 7.0, 7.7, 7.9, 8.5, 8.8, 12.5 Complete the back-to-back stem plot for data set B by adding the numbers that belong in each class below, using a class width of 1.  Do not enter spaces between the numbers. If...
The data below represent commute times​ (in minutes) and scores on a​ well-being survey. Complete parts​...
The data below represent commute times​ (in minutes) and scores on a​ well-being survey. Complete parts​ (a) through​ (d) below. Commute Time​ (minutes), x 55 1515 3030 3535 5050 8484 105105 ​Well-Being Index​ Score, y 69.169.1 67.867.8 66.266.2 65.865.8 64.564.5 62.362.3 59.959.9 ​(a) Find the​ least-squares regression line treating the commute​ time, x, as the explanatory variable and the index​ score, y, as the response variable. ModifyingAbove y with caretyequals=nothingxplus+left parenthesis nothing right parenthesis ​(Round to three decimal places as​...
The data below represent commute times​ (in minutes) and scores on a​ well-being survey. Complete parts​...
The data below represent commute times​ (in minutes) and scores on a​ well-being survey. Complete parts​ (a) through​ (d) below. Commute Time​ (minutes), x 5 15 30 40 50 84 105 ​Well-Being Index​ Score, y 68.9 67.6 65.8 64.9 64.0 61.5 58.8 ​(a) Find the​ least-squares regression line treating the commute​ time, x, as the explanatory variable and the index​ score, y, as the response variable. ModifyingAbove y with caret equalsnothingxplusleft parenthesis nothing right parenthesis ​(Round to three decimal places...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT